Caulking is typically used to provide a resilient seal between two adjacent structures, such as a window frame and a brick wall, to prevent water and air from entering the gap between the two adjacent structures. Although caulking is desirable, it is often difficult to dispense the viscous caulk into the gap between the structures with the straight, tapered caulk tube conventionally provided with the caulk container. It would be a benefit, therefore, to have a caulk tube nozzle that was attachable over the caulk tube of the caulk container and which was sufficiently flexible to allow a tapered nozzle end portion of the caulk tube nozzle to be oriented at a number of desirable angles with respect to a caulk tube attachment portion of the caulk tube nozzle. Additionally, because caulk is highly viscous, it could be difficult to maintain a caulk tube nozzle on the caulk tube. It would be a further benefit, therefore, to have a caulk tube nozzle that included a number of caulk tube gripping structures that could cut into and engage the sidewall of the caulk tube to prevent the caulk tube nozzle from being forced off the caulk tube by caulk flowing through the caulk tube nozzle.